%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU424+3 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:53 AM UTC 2025
% Result : Theorem 213.07s 213.39s
% Output : Proof 214.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU424+3 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:13:55 EDT 2025
% 0.18/0.33 % CPUTime :
% 213.07/213.39 % SZS status Theorem
% 213.07/213.39 % SZS output start Proof
% 213.07/213.39 tff(m1_subset_1_type, type, (
% 213.07/213.39 m1_subset_1: ( $i * $i ) > $o)).
% 213.07/213.39 tff(k1_zfmisc_1_type, type, (
% 213.07/213.39 k1_zfmisc_1: $i > $i)).
% 213.07/213.39 tff(tptp_fun_B_6302_type, type, (
% 213.07/213.39 tptp_fun_B_6302: $i)).
% 213.07/213.39 tff(a_4_0_relset_2_type, type, (
% 213.07/213.39 a_4_0_relset_2: ( $i * $i * $i * $i ) > $i)).
% 213.07/213.39 tff(tptp_fun_D_6303_type, type, (
% 213.07/213.39 tptp_fun_D_6303: $i)).
% 213.07/213.39 tff(tptp_fun_C_6301_type, type, (
% 213.07/213.39 tptp_fun_C_6301: $i)).
% 213.07/213.39 tff(tptp_fun_A_6300_type, type, (
% 213.07/213.39 tptp_fun_A_6300: $i)).
% 213.07/213.39 tff(m2_relset_1_type, type, (
% 213.07/213.39 m2_relset_1: ( $i * $i * $i ) > $o)).
% 213.07/213.39 tff(v1_xboole_0_type, type, (
% 213.07/213.39 v1_xboole_0: $i > $o)).
% 213.07/213.39 tff(1,plain,
% 213.07/213.39 (((~v1_xboole_0(A!6300)) & (m1_subset_1(C!6301, k1_zfmisc_1(A!6300)) & (~((~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))))))) <=> ((~v1_xboole_0(A!6300)) & m1_subset_1(C!6301, k1_zfmisc_1(A!6300)) & (~((~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))))))),
% 213.07/213.39 inference(rewrite,[status(thm)],[])).
% 213.07/213.39 tff(2,plain,
% 213.07/213.39 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))))),
% 213.07/213.39 inference(rewrite,[status(thm)],[])).
% 213.07/213.39 tff(3,plain,
% 213.07/213.39 ((~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m2_relset_1(D, A, B) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))))),
% 213.07/213.39 inference(rewrite,[status(thm)],[])).
% 213.07/213.39 tff(4,axiom,(~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => ![D: $i] : (m2_relset_1(D, A, B) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t18_relset_2')).
% 213.07/213.39 tff(5,plain,
% 213.07/213.39 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 213.07/213.39 tff(6,plain,
% 213.07/213.39 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 213.07/213.39 tff(7,plain,
% 213.07/213.39 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 213.07/213.39 tff(8,plain,
% 213.07/213.39 (~![A: $i] : (v1_xboole_0(A) | ![B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | ![D: $i] : ((~m2_relset_1(D, A, B)) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 213.07/213.39 tff(9,plain,
% 213.07/213.39 ((~v1_xboole_0(A!6300)) & m1_subset_1(C!6301, k1_zfmisc_1(A!6300)) & (~((~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302)))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 213.07/213.39 tff(10,plain,
% 213.07/213.39 (~((~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))))),
% 213.07/213.39 inference(and_elim,[status(thm)],[9])).
% 213.07/213.39 tff(11,plain,
% 213.07/213.39 (~m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302)))),
% 213.07/213.39 inference(or_elim,[status(thm)],[10])).
% 213.07/213.39 tff(12,plain,
% 213.07/213.39 (m2_relset_1(D!6303, A!6300, B!6302)),
% 213.07/213.39 inference(or_elim,[status(thm)],[10])).
% 213.07/213.39 tff(13,plain,
% 213.07/213.39 (m1_subset_1(C!6301, k1_zfmisc_1(A!6300))),
% 213.07/213.39 inference(and_elim,[status(thm)],[9])).
% 213.07/213.39 tff(14,plain,
% 213.07/213.39 (~v1_xboole_0(A!6300)),
% 213.07/213.39 inference(and_elim,[status(thm)],[9])).
% 213.07/213.39 tff(15,plain,
% 213.07/213.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 213.07/213.39 inference(bind,[status(th)],[])).
% 213.07/213.39 tff(16,plain,
% 213.07/213.39 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 213.07/213.39 inference(quant_intro,[status(thm)],[15])).
% 213.07/213.39 tff(17,plain,
% 213.07/213.39 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B)) <=> (~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) <=> (~(~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) <=> (v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))), rewrite(((v1_xboole_0(A) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 213.07/213.39 inference(bind,[status(th)],[])).
% 213.07/213.39 tff(18,plain,
% 213.07/213.39 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 213.07/213.39 inference(quant_intro,[status(thm)],[17])).
% 213.07/213.39 tff(19,plain,
% 213.07/213.39 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 213.07/213.39 inference(rewrite,[status(thm)],[])).
% 213.07/213.39 tff(20,plain,
% 213.07/213.39 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) <=> ((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))), (((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> (((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), (((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))))),
% 213.07/213.39 inference(bind,[status(th)],[])).
% 213.07/213.39 tff(21,plain,
% 213.07/213.39 (![A: $i, B: $i, C: $i, D: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 213.07/213.39 inference(quant_intro,[status(thm)],[20])).
% 213.07/213.39 tff(22,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A))) & m2_relset_1(D, A, B)) => m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s8_domain_1__e1_22__relset_2')).
% 213.07/213.39 tff(23,plain,
% 213.07/213.39 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 213.07/213.39 tff(24,plain,
% 213.07/213.39 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 213.07/213.39 tff(25,plain,(
% 213.07/213.39 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(C, k1_zfmisc_1(A)) & m2_relset_1(D, A, B))) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))))),
% 213.07/213.39 inference(skolemize,[status(sab)],[24])).
% 213.07/213.39 tff(26,plain,
% 213.07/213.39 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[25, 18])).
% 213.07/213.39 tff(27,plain,
% 213.07/213.39 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 213.07/213.39 inference(modus_ponens,[status(thm)],[26, 16])).
% 213.07/213.39 tff(28,plain,
% 213.07/213.39 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(A!6300) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(A!6300) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))))),
% 213.07/213.39 inference(rewrite,[status(thm)],[])).
% 213.07/213.39 tff(29,plain,
% 213.07/213.39 ((v1_xboole_0(A!6300) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300)))) <=> (v1_xboole_0(A!6300) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))))),
% 214.60/214.95 inference(rewrite,[status(thm)],[])).
% 214.60/214.95 tff(30,plain,
% 214.60/214.95 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(A!6300) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(A!6300) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302)))))),
% 214.60/214.95 inference(monotonicity,[status(thm)],[29])).
% 214.60/214.95 tff(31,plain,
% 214.60/214.95 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(A!6300) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(A!6300) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))))),
% 214.60/214.95 inference(transitivity,[status(thm)],[30, 28])).
% 214.60/214.95 tff(32,plain,
% 214.60/214.95 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(A!6300) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))))),
% 214.60/214.96 inference(quant_inst,[status(thm)],[])).
% 214.60/214.96 tff(33,plain,
% 214.60/214.96 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | m1_subset_1(a_4_0_relset_2(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(B))) | (~m2_relset_1(D, A, B)) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(A!6300) | (~m1_subset_1(C!6301, k1_zfmisc_1(A!6300))) | (~m2_relset_1(D!6303, A!6300, B!6302)) | m1_subset_1(a_4_0_relset_2(A!6300, B!6302, C!6301, D!6303), k1_zfmisc_1(k1_zfmisc_1(B!6302)))),
% 214.60/214.96 inference(modus_ponens,[status(thm)],[32, 31])).
% 214.60/214.96 tff(34,plain,
% 214.60/214.96 ($false),
% 214.60/214.96 inference(unit_resolution,[status(thm)],[33, 27, 14, 13, 12, 11])).
% 214.60/214.96 % SZS output end Proof
% 215.21/215.54 % E exiting
%------------------------------------------------------------------------------